Question

se f(x)=x+2 e g(x)=x(ao quadrado) -2, quais os valores de x para que f(g(x)) = g(f(x))?

Answer 1

$f(g(x)) = g(f(x)) \\\\ g(x)+2 = [f(x)]^{2}-2 \\\\ x^{2}-2+2 = (x+2)^{2}-2 \\\\ x^{2} = x^{2}+4x+4-2 \\\\ 4x = -2 \\\\ \boxed{\boxed{x = -\frac{1}{2}}}$